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A367240
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^2)^3.
4
1, 1, 5, 29, 192, 1372, 10314, 80390, 643774, 5264984, 43788393, 369221844, 3149085162, 27119598885, 235495141963, 2059677411141, 18127763268114, 160433599528417, 1426870597505859, 12746368353418175, 114316604199957112, 1028937342955189009
OFFSET
0,3
FORMULA
If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).
PROG
(PARI) a(n, s=3, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 11 2023
STATUS
approved